Answer:
x = 12
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
g(x) = 1/2x - 11
g(x) = -5
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute: -5 = 1/2x - 11
- Isolate <em>x</em> term: 6 = 1/2x
- Isolate <em>x</em>: 12 = x
- Rewrite: x = 12
Answer:985,600
Step-by-step explanation:
Answer:
New area is 175 42/45 feet ²
Step-by-step explanation:
Given data
Length l= 15 1/4
To proper fraction = 61/4 feet
Width w= 8 11/15
To proper fraction = 131/15 feet
Extention = 1 2/3
To proper fraction = 5/3
Dimensions of new rectangle
Length =61/4+5/3 = 183+20/12
LCM = 12 = 203/12
Width = 131/15+5/3= 131+25/15
LCM = 15 = 156/15
Area = 203/12*156/15= =31668/180
=31668/180
= 7917/45
= 175 42/45 feet ²
Lily made $75.36 more than Layla did. If Layla raised her price to $1.00, she would still not make more money than Lily.
Use a proportion to find the number of cupcakes Lily makes in 8 hours. She bakes 7 cupcakes in 10 minutes; we want to know how many she makes in 8(60)=480 (since there are 8 hours and each hour is 60 minutes):
7/10 = x/480
Cross multiply:
7*480 = 10*x
3360 = 10x
Divide both sides by 10:
3360/10 = 10x/10
336 = x
Lily bakes 336 cupcakes.
She sells 2/3 of these; 2/3(336) = 2/3(336/1) = 672/3 = 224 cupcakes sold.
Each cupcake is sold for $1.29; 224(1.29) = 288.96
To find the number of cupcakes Layla makes in 8 hours, we set up a different proportion. We know she bakes 8 cupcakes in 12 minutes; we want to know how many she bakes in 8(60) = 480 minutes:
8/12 = x/480
8*480 = 12*x
3840 = 12x
Divide both sides by 12:
3840/12 = 12x/12
320 = x
She bakes 320 cupcakes. She sells 75% of those; 75% = 75/100 = 0.75:
0.75(320) = 240
Each of those 240 cupcakes sells for $0.89:
0.89(240) = 213.60
This means Lily makes 288.96-213.60 = 75.36 more than Layla.
If Layla raised her price to $1.00, she would make 1(240) = $240; this is still less than Lily.
Answer:
Once the equation is in standard form, factor the quadratic expression. 2x2 + 7x + 3 = 0 (2x + 1)(x + 3) = 0. Using the Zero Product Property set ...
2x2 + 7x = -3
2x2 + 7x + 3 = 0
Once the equation is in standard form, factor the quadratic expression.
2x2 + 7x + 3 = 0
(2x + 1)(x + 3) = 0
Using the Zero Product Property set each factor equal to 0 and solve for x.
2x + 1 = 0
2x + 1 - 1 = 0 - 1 x + 3 = 0
2x = -1 x + 3 - 3 = 0 - 3
2x 2 = -1 2 x = -3
x = -1 2
The solutions to the equation are -1 2 and -3.
